# Publications

### Recent Publications

1. ArXiv A Poly-algorithmic Approach to Quantifier Elimination, with James H. Davenport, and Zak P. Tonks (submitted).
2. ArXiv Lazard-style CAD and Equational Constraints, with James H. Davenport, Akshar Nair, and Gregory Sankaran (submitted).
3. ArXiv A Unified Approach to Unimodality of Gaussian Polynomials, with Christoph Koutschan and Elaine Wong (submitted).
4. ArXiv Proofs of Modulo 11 and 13 Cylindric Kanade-Russell Conjectures for $A_2$ Rogers-Ramanujan Type Identities (submitted) Documentation
5. ArXiv Sequences in Overpartitions, with George E. Andrews. Ramanujan J (2023). https://doi.org/10.1007/s11139-022-00685-y
6. Artificial Conflict Sampling for Real Satisfiability Problems, with James H. Davenport (accepted, 24th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC) 2022, IEEE Electronic Publication Paper Id: 1668357797545)
7. SMT-Solving Induction Proofs of Inequalities, with James H. Davenport and Matthew England (accepted, 7th SC^2 Workshop, Federated Logic Conference 2022 Proceedings )
8. ArXiv On Finite Analogs of Schmidt’s Problem and Its Variants, with Alexander Berkovich (submitted)
9. ArXiv Weighted Cylindric Partitions, with Walter Bridges. Journal of Algebraic Combinatorics volume 56, pages 1309–1337 (2022)
10. CEUR Practical Evaluation of Quantifier Elimination Methods, with James H. Davenport, and Zak P. Tonks. (accepted, 6th SC^2 Workshop Proceedings, SIAM Conference on Applied Algebraic Geometry Conference 2021 Proceedings)
11. ArXiv New infinite hierarchies of polynomial identities related to the Capparelli partition theorems, with Alexander Berkovich. J. Math. Anal. Appl. 506 (2022), no. 2, Paper No. 125678, 18 pp.
12. ArXiv Cylindric Partitions and some new $A_2$ Rogers-Ramanujan Identities, with Sylvie Corteel and Jehanne Dousse. Proc. Amer. Math. Soc. 150 (2022), 481-497.
13. ArXiv Reflecting (on) the modulo 9 Kanade-Russell (conjectural) identities, with Wadim Zudilin. Séminaire Lotharingien de Combinatoire, B85e (2021), 17 pp
14. ArXiv On Double Sum Generating Functions in Connection with Some Classical Partition Theorems. Disc. Math J. Volume 344, Issue 11, (2021), 112562
15. ArXiv qFunctions – A Mathematica package for q-series and partition theory applications, with Jakob Ablinger. Journal of Symbolic Computation 107 (2021), 145-166.
16. ArXiv Logconcavity results for a biparametric and an elliptic extension of the q-binomial coefficients, with Michael Schlosser and  Koushik Senapati. Int. J. Number Theory 17 (2021), no. 3, 787–804.
17. ArXiv Where do the maximum absolute q-series coefficients of $(1-q)(1-q^2)(1-q^3)\dots(1-q^{n-1})(1-q^n)$ occur?, with Alexander Berkovich.
18. ArXiv On a weighted spin of the Lebesgue Identity. Mathematical Aspects of Computer and Information Sciences. MACIS 2019. Lecture Notes in Computer Science, vol 11989. Springer, Cham. https://doi.org/10.1007/978-3-030-43120-4_20
19. ArXiv A Polynomial Identity Implying Schur’s Partition Theorem. Proc. Amer. Math. Soc. 148 (2020), 3307-3324
20. ArXiv Refined q-Trinomial Coefficients and Two Infinite Hierarchies of q-Series Identities, with Alexander Berkovich. Algorithmic Combinatorics: Enumerative Combinatorics, Special Functions and Computer Algebra. Texts & Monographs in Symbolic Computation (A Series of the Research Institute for Symbolic Computation, Johannes Kepler University, Linz, Austria). Springer, Cham. https://doi.org/10.1007/978-3-030-44559-1_4
21. ArXiv Elementary Polynomial Identities Involving q-Trinomial Coefficients, with Alexander Berkovich. Ann. Comb. 23 (2019), 549–560.
22. ArXiv Polynomial Identities Implying Capparelli’s Partition Theorems, with Alexander Berkovich. J. Number Theory 201 (2019), 77-107.
23. ArXiv Some Elementary Partition Inequalities and Their Implications, with Alexander Berkovich. Ann. Comb. 23 (2019), 263-284.
24. ArXiv Weighted Rogers-Ramanujan Partitions and Dyson Crank.  Ramanujan J. 46 (2018), no. 2, 579–591.
25. ArXiv On Some Polynomials and Series of Bloch-Polya Type, with Alexander Berkovich. Proc. Amer. Math. Soc. 146 (2018), no. 7, 2827–2838.
26. ArXiv New Weighted Partition Theorems with the Emphasis on the Smallest Part of Partitions, with Alexander Berkovich. ALLADI 60 2016: Analytic Number Theory, Modular Forms and q-Hypergeometric Series (2017) pp 69-94 Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 221)
27. ArXiv Variation on a theme of Nathan Fine. New weighted partition identities, with Alexander Berkovich. J. Number Theory 176 (2017), 226–248.
28. ArXiv On partitions with fixed number of even-indexed and odd-indexed odd parts, with Alexander Berkovich. J. Number Theory 167 (2016), 7–30.
29. ArXiv A New Companion to Capparelli’s Identities, with Alexander Berkovich. Adv. in Appl. Math. 71 (2015), 125–137.

### Extended Abstracts

1. qFunctions: A Mathematica package for partition theory applications, and its future, Computer Algebra in Scientific Computing 2021 (CASC 21) Proceedings.
2. ArXiv The DEWCAD Project: Pushing Back the Doubly Exponential Wall of Cylindrical Algebraic Decomposition, with Russell Bradford, James H. Davenport, Matthew England, and Amirhossein Sadeghimanesh. ISSAC 2021 https://dl.acm.org/doi/abs/10.1145/3511528.3511538
3. On q-Rising Factorials and the Necessity of Shared Memory Calculations. Austrian High-Performance-Computing meeting (AHPC2020), Publisher: Institute of Science and Technology Austria, Klosterneuburg Austria, Editors: Alois Schlögl et al. ISBN: 978-3-99078-004-6

### Popular Math Publications

1. Parçalanış Teorisine Davet, Matematik Dünyası Yıl 29, Sayı 119, Aralık 2022 (Eng. Invitation to Theory of Partitions, World of Mathematics Journal, year 29, vol 119, December 2022)

### Soon to be Public

• On more conjectural identities modulo 16 and 20, joint with George E. Andrews
• Counting  on 4-decorated diagrams.

### Editorial Work

1. Guest Editor: Mathematics in Computer Science – ACA 2022 Special Issue, with Tülay Ayyıldız Akoğlu, Ilias Kotsireas and Zafeirakis Zafeirakopoulos, published by Birkhauser Springer.
2. Editor: 7th SC^2 Workshop Proceedings (SC^2 2022) with Haniel Barbosa.
3. Guest Editor: Mathematics in Computer ScienceACA 2021 (Virtual Online) Special Issue, with Ilias Kotsireas and Dimitris Simos, published by Birkhauser Springer.